Voltage @z=−l | V i n c = V + ( z = − l ) = V i n 1 + Γ L e − 2 j β l | V r e f l e c t e d = V − ( z = − l ) = V i n ( 1 + Γ L e − 2 j β l ) Γ L e − 2 j β l | Vin |
Current @z=−l | I i n c = I + ( z = − l ) = V i n Z 0 ⋅ ( 1 + Γ L e − 2 j β l ) | I r e f l e c t e d = I − ( z = − l ) = − V i n Z 0 ⋅ ( 1 + Γ L e − 2 j β l ) Γ L e − 2 j β l | I i n = I + ( z = − l ) + I − ( z = − l ) = V i n Z 0 ⋅ 1 − Γ L e − 2 j β l 1 + Γ L e − 2 j β l |
Power @z=−l | P i n c = 1 2 R e ( V i n c ⋅ I i n c * ) = 1 2 R e ( V i n 1 + Γ L e − 2 j β l ⋅ ( V i n Z 0 ⋅ ( 1 + Γ L e − 2 j β l ) ) * ) = | V i n | 2 2 Z 0 1 | 1 + Γ L e − 2 j β l | 2 | P r e f l e c t e d = 1 2 R e ( V r e f l e c t e d ⋅ I r e f l e c t e d * ) = 1 2 R e ( V i n ( 1 + Γ L e − 2 j β l ) Γ L e − 2 j β l ⋅ ( V i n ) * Z 0 ⋅ ( 1 + Γ L . e 2 j β l ) Γ L * e 2 j β l ) = − | V i n | 2 2 Z 0 ⋅ | Γ L | 2 | 1 + Γ L e − 2 j β l | 2 | P i n = 1 2 R e ( V i n ⋅ I i n * ) = | V i n | 2 2 Z 0 R e ( ( 1 + Γ L e − 2 j β l ) ( 1 + Γ L e − 2 j β l ) ⋅ ( 1 − Γ L e − 2 j β l ) * ( 1 + Γ L e − 2 j β l ) * ) = | V i n | 2 2 Z 0 ⋅ 1 − | Γ L | 2 | 1 + Γ L e − 2 j β l | 2 |